6 citations · 13 across the 6 of their papers we have counts for
6 papers
Compact bordered Riemannian surfaces as vibrating membranes: an estimate à la Hersch-Yang-Yau-Fraser-Schoen
Alexandre Gabard
We try to present an estimate relating the first Dirichlet and Neumann eigenvalues of a compact bordered Riemannian surface.
Hairiness of -bounded surfaces with non-zero Euler characteristic
Alexandre Gabard
A little complement concerning the dynamics of non-metric manifolds is provided, by showing that any flow on an -bounded surface with non-zero Euler character has a fixed point.
Dynamics of non-metric manifolds
Alexandre Gabard, David Gauld
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
Jordan and Schoenflies in non-metrical analysis situs
Alexandre Gabard, David Gauld
We show that both, the Jordan curve theorem and the Schoenflies theorem extend to non-metric manifolds (at least in the two-dimensional context), and conclude by some dynamical app…
Foliations on non-metrisable manifolds: absorption by a Cantor black hole
Mathieu Baillif, Alexandre Gabard, David Gauld
We investigate contrasting behaviours emerging when studying foliations on non-metrisable manifolds. It is shown that Kneser's pathology of a manifold foliated by a single leaf can…
A separable manifold failing to have the homotopy type of a CW-complex
Alexandre Gabard
We show that the Prüfer surface, which is a separable non-metrizable 2-manifold, has not the homotopy type of a CW-complex. This will follow easily from J. H. C. Whitehead's result…